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Types of equilibria
- Homogeneous Equilibria
This occurs in reactions in which all reactants and products are in the same liquid or gas phase.
A ↔ B
A can be in gas or in liquid form and B can be gas or in liquid form
- Kc = [B]/[A]
- Or
- Kp =PB/PA
Kc or Kp is used depending on whether A and B are in solution or in gas phase. The concepts of Kc isbased on molar concentrations of solution whereas Kp, is based on partial pressures of gaseous species.
In general Kc ≠ Kp unless the number of moles of gas does not change during the reaction.
If the equilibrium expression does not contain different powers of [A] or [B] in the numerator or denominator, the ration of [B]/[A] is the same as that of PB/PA. If there are different powers of [B] or A in the expression, then the ratio changes.
Heterogeneous Equilibria
This occurs in reactions in which the reactants and the products are not in the same physical state or and in different phases.
If a solid or liquid is part of a chemical equilibrium, its “concentration” is taken as unity and may be eliminated from the equilibrium expression.
NH3(g) + HCl(g) ↔ NH4Cl(s)
Keq = [NH4Cl] / [NH3]·[HCl]
Since NH4Cl is a solid, its effective concentration in the reaction does not change as long as some solid is present. Since [NH4Cl] is constant, it can be eliminated from the right side of the equation and incorporated into the Keq constant, which them becomes
Keq = 1/[NH3]·[HCl] if the molar concentrations of the gases will be expressed, or
Kp = 1/PNH3·PHCl if the gas pressures will be expressed.
Example: How will [NH3] vary in the system as [HCl] increases or decreases?
Multiple Equilibria
The Keq values from two or more successive reactions are simply multiplied together if the reactions can be added together to make one net reaction.
- For A → B Keq = [A]/[B] and
- For B → C, Keq = [B]/[C]
Adding the two equations together gives
A → C with Keq = [A]/[C]
The same Keq expression would have been obtained by multiplying together the two first K values. Applications include stepwise dissociation of polyprotic acids such as H3PO4
H3PO4↔ H2PO4-1 + H+1 K1= [H3PO4]/[ H2PO4-1] · [H+1] H3PO4]/[ H2PO4-1] · [H+1]K2= etc HPO4-2 ↔ PO4-3 + H+1 K3= etc |
K1 |
= [ |
The allover K = K1 · K2 · K3 for the equation
H3PO4 → PO4-3 + 3H+1
The Form of K and The Equilibrium Constant
The K for an equilibrium reaction is the reciprocal of the K for the reverse reaction. Therefore it is important to specify what reaction the K meant to represent.
For A ↔ B + C,
- Kf = [B][C]
- [A]
- For B + C ↔ A,
- Kr = [A]
- [B][C]
ThereforeKf xKr = [A][B][C]/[A][B][C] = 1
Remember that the reactant and product concentrations in the Keq expression are raised to the power equal to their coefficients. What happens if the equation is written in more than one way?
H2(g) + I2(g) ↔ 2HI(g) |
K1 = [H2][I2] /[HI]2 |
½H2(g) + ½I2(g)↔HI(g) |
K2 = [H2] ½ [I2]½ /[HI] |
Will the Keq values be different or the same for the two ways of writing the same equation? Consider both as representing the same system. Set [H2] = 0.020M, [I 2] = 0.030M and [HI] = 0.010M. Calculate both Keq values.
- K1 = [H2][I2] /[HI]2 = (0.020M)(0.030M)/0.010M)2
- = 6.0
- K2 = [H2]½ [I2]½ /[HI] = (0.020M)½ (0.030M)½ /(0.010M)1
- = 2.4 (or 6½)
K1 = (K2)2
Both Keq values will give the same reactant and product concentrations when applied to the corresponding equations.
Relation Between Chemical Kinetics and Chemical Equilibrium
There is a direct relationship between the rate constant for the forward and reverse directions of a chemical reaction and the equilibrium constant for that reaction. That stands to reason because a large forward rate constant will lead to a larger K. A large backward rate constant will lead to a small K. for a first order chemical reaction,
A ↔ B, ratef =kf [A] and Kf = [B]/[A]
For the reverse reaction, B ↔ A, rater = kr[B] Kr = [A]/[B]
By definition, at equilibrium the two rates, but not the kf and the kr, are the same. (Remember that the rates depend on the k values and on the A and B concentrations.)
If ratef = rater, then kf [A] = kr[B]
kf /kr = [A]/[B] which is equal to the equilibrium constant, Kf. A large forward rate constant leads to a high rate of formation of B and a large value of Kf. Similarly, kr / kf = [B]/[A] = Kr.